gradient_checker_v2.py

# Copyright 2015 The TensorFlow Authors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ==============================================================================
"""Gradient checker for functions.

The gradient checker verifies numerically that an function properly
computes the gradients
"""
import numpy as np

from tensorflow.python.eager import backprop
from tensorflow.python.eager import context
from tensorflow.python.framework import dtypes
from tensorflow.python.framework import indexed_slices
from tensorflow.python.framework import ops
from tensorflow.python.ops import array_ops
from tensorflow.python.platform import tf_logging as logging
from tensorflow.python.util.tf_export import tf_export


def _product(t):
  if isinstance(t, int):
    return t
  else:
    y = 1
    for x in t:
      y *= x
    return y


def _eval_indexed_slices(a):
  """Converts IndexedSlices to IndexedSlicesValue with numpy indices/values.

  When eager execution is enabled, converts IndexedSlices
  to IndexedSlicesValue with numpy indices/values.

  Args:
    a: any value.

  Returns:
    If a is IndexedSlices and eager execution is enabled, calls numpy() on a's
    fields. Otherwise returns a unchanged.
  """
  if (isinstance(a, indexed_slices.IndexedSlices) and
      context.executing_eagerly()):
    return indexed_slices.IndexedSlicesValue(
        indices=[x.numpy() for x in a.indices],
        values=[x.numpy() for x in a.values],
        dense_shape=a.dense_shape)
  return a


def _to_numpy(a):
  """Converts Tensors, EagerTensors, and IndexedSlicesValue to numpy arrays.

  Args:
    a: any value.

  Returns:
    If a is EagerTensor or Tensor, returns the evaluation of a by calling
    numpy() or run(). If a is IndexedSlicesValue, constructs the corresponding
    dense numpy array. Otherwise returns a unchanged.
  """
  if isinstance(a, ops.EagerTensor):
    return a.numpy()
  if isinstance(a, ops.Tensor):
    sess = ops.get_default_session()
    return sess.run(a)
  if isinstance(a, indexed_slices.IndexedSlicesValue):
    arr = np.zeros(a.dense_shape)
    assert len(a.values) == len(a.indices), (
        "IndexedSlicesValue has %s value slices but %s indices\n%s" %
        (a.values, a.indices, a))
    for values_slice, index in zip(a.values, a.indices):
      assert 0 <= index < len(arr), (
          "IndexedSlicesValue has invalid index %s\n%s" % (index, a))
      arr[index] += values_slice
    return arr
  return a


def _prepare(f, xs_dtypes, xs_shapes):
  """Return a function that executes 'f'.

    In TF 2.x, this is the same as `f`.
    In TF 1.x, returns a Python function that executes the graph defined by `f`
    in a Session.

  Args:
    f: the function.
    xs_dtypes: dtypes of f's arguments.
    xs_shapes: shapes of f's arguments.

  Returns:
  """
  if context.executing_eagerly():

    def decorated_eager(*xs_data):
      return f(*map(ops.convert_to_tensor, xs_data))

    return decorated_eager
  xs = [
      array_ops.placeholder(x_dtype, shape=x_shape)
      for x_dtype, x_shape in zip(xs_dtypes, xs_shapes)
  ]
  y = f(*xs)
  sess = ops.get_default_session()

  def decorated_graph(*xs_data):
    xs_data = [_to_numpy(a) for a in xs_data]
    return sess.run(y, feed_dict=dict(zip(xs, xs_data)))

  return decorated_graph


def _compute_theoretical_jacobian(f, y_shape, y_dtype, xs, param):
  """Computes the theoretical Jacobian for f regarding xs[param].

  One can think of the relation among f, xs and y as y = f(xs).

  Args:
    f: the function.
    y_shape: the shape of the result.
    y_dtype: the dtype of the result.
    xs: a list of tensors.
    param: the index of the target parameter.

  Returns:
    A 2-d numpy array representing the Jacobian. It has "y_size" rows
    and "x_size" columns where "x_size" is the number of elements in xs[param]
    and "y_size" is the number of elements in the result.

  Raises:
    ValueError: If result is empty but the gradient is nonzero.
  """
  x = xs[param]
  # Complex vectors are treated as vectors of twice as many reals.
  x_shape = tuple(x.shape) + (2,) if x.dtype.is_complex else x.shape
  y_factor = 2 if y_dtype.is_complex else 1

  # To compute the jacobian, we treat x and y as one-dimensional vectors.
  x_size = _product(x_shape)
  x_val_size = _product(x_shape[1:])  # This is used for sparse gradients
  y_size = _product(y_shape) * y_factor

  # Allocate 2-D Jacobian, with y dimensions smashed into the first
  # dimension and x dimensions smashed into the second.
  jacobian = np.zeros((y_size, x_size), dtype=x.dtype.real_dtype.as_numpy_dtype)

  # For each of the entry of dy, we set this to be 1 and
  # everything else to be 0 and compute the gradients -- this will give us one
  # row of the Jacobian matrix.
  dy_data = np.zeros(y_shape, dtype=y_dtype.as_numpy_dtype)
  dy_data_flat = dy_data.ravel().view(y_dtype.real_dtype.as_numpy_dtype)
  grad_fn_unprep = backprop.gradients_function(f, [param])
  grad_fn = _prepare(lambda dy, *xs: grad_fn_unprep(*xs, dy=dy),
                     [y_dtype] + [z.dtype for z in xs],
                     [None] + [z.shape for z in xs])
  for row in range(y_size):
    dy_data_flat[row] = 1
    grad = _to_numpy(grad_fn(dy_data, *xs)[0])
    grad = _eval_indexed_slices(grad)
    if isinstance(grad, indexed_slices.IndexedSlicesValue):
      for i, v in zip(grad.indices, grad.values):
        c_begin = i * x_val_size
        c_end = c_begin + x_val_size
        jacobian[row, c_begin:c_end] += v.flat
    elif grad is not None:
      jacobian[row, :] = grad.ravel().view(jacobian.dtype)
    # This reset of `dy_data_flat` needs to happen after `grad` is copied to
    # `jacobian` because `grad` and `dy_data_flat` may share memory.
    dy_data_flat[row] = 0

  # If the output is empty, run the gradients at least once and make sure
  # they produce zeros.
  if y_size == 0:  # don't use 'not y_size', because y_size may not be an int
    grad = _to_numpy(grad_fn(dy_data, *xs)[0])
    if grad.shape != x.shape:
      raise ValueError("Empty gradient has wrong shape: expected %s, got %s" %
                       (x.shape, grad.shape))
    if np.any(grad):
      raise ValueError("Empty tensor with nonzero gradients")

  logging.vlog(1, "Theoretical Jacobian =\n%s", jacobian)
  return jacobian


def _compute_numeric_jacobian(f, y_size, y_dtype, xs, param, delta):
  """Computes the numeric Jacobian for f regarding xs[param].

  One can think of the relation among f, xs and y as y = f(xs).

  Args:
    f: the function.
    y_size: the number of elements of the result.
    y_dtype: the dtype of the result.
    xs: a list of tensors.
    param: the index of the target parameter.
    delta: the amount of perturbation we give to the input.

  Returns:
    A 2-d numpy array representing the Jacobian. It has "y_size" rows
    and "x_size" columns where "x_size" is the number of elements in xs[param]
    and "y_size" is the number of elements in the result.
  """
  x_shape = xs[param].shape
  x_dtype = xs[param].dtype

  # To compute the jacobian, we treat x and y as one-dimensional vectors
  x_size = _product(x_shape) * (2 if x_dtype.is_complex else 1)
  y_size = y_size * (2 if y_dtype.is_complex else 1)
  x_dtype = x_dtype.real_dtype.as_numpy_dtype
  y_dtype = y_dtype.real_dtype.as_numpy_dtype

  xs_dtypes = [x.dtype for x in xs]
  xs_shapes = [x.shape for x in xs]
  # Converts xs to numpy arrays to do in-place perturbation.
  # Calls asarray() to avoid copying in ravel() later.
  xs = [np.asarray(_to_numpy(x)) for x in xs]
  x = xs[param]

  # Make sure we have the right types
  scale = np.asarray(2 * delta, dtype=y_dtype)[()]

  jacobian = np.zeros((y_size, x_size), dtype=x_dtype)

  # For each of the entry of x, we slightly perturbs this by adding and
  # subtracting a delta and then compute difference between the outputs. This
  # will give us one column of the Jacobian matrix.
  f = _prepare(f, xs_dtypes, xs_shapes)
  for col in range(x_size):
    original = x.ravel().view(x_dtype)[col]
    x.ravel().view(x_dtype)[col] += delta
    y_pos = _to_numpy(f(*xs))
    x.ravel().view(x_dtype)[col] = original
    x.ravel().view(x_dtype)[col] -= delta
    y_neg = _to_numpy(f(*xs))
    x.ravel().view(x_dtype)[col] = original
    diff = (y_pos - y_neg) / scale
    jacobian[:, col] = diff.ravel().view(y_dtype)

  logging.vlog(1, "Numeric Jacobian =\n%s", jacobian)
  return jacobian


def _compute_gradient(f, y_shape, y_dtype, xs, param, delta):
  """Computes the theoretical and numerical jacobian."""
  x = xs[param]
  t = x.dtype
  allowed_types = [
      dtypes.float16, dtypes.bfloat16, dtypes.float32, dtypes.float64,
      dtypes.complex64, dtypes.complex128
  ]
  assert t.base_dtype in allowed_types, ("Cannot compute gradient for "
                                         "unsupported type %s of argument %s" %
                                         (t.name, param))
  t2 = y_dtype
  assert t2.base_dtype in allowed_types, ("Cannot compute gradient for "
                                          "unsupported type %s of y" % t2.name)
  y_size = _product(y_shape)
  jacob_t = _compute_theoretical_jacobian(f, y_shape, y_dtype, xs, param)
  jacob_n = _compute_numeric_jacobian(f, y_size, y_dtype, xs, param, delta)
  return jacob_t, jacob_n


def _compute_gradient_list(f, xs, delta):
  """Compute gradients for a list of x values."""
  # convert xs to tensors so that dtype and shape have uniform types
  xs = [ops.convert_to_tensor(x) for x in xs]
  # run the function to get info of the result
  xs_dtypes = [x.dtype for x in xs]
  xs_shapes = [x.shape for x in xs]
  f_temp = _prepare(f, xs_dtypes, xs_shapes)
  y = f_temp(*xs)
  return tuple(
      zip(*[
          _compute_gradient(f, y.shape, dtypes.as_dtype(y.dtype), xs, i, delta)
          for i in range(len(xs))
      ]))


@tf_export("test.compute_gradient", v1=[])
def compute_gradient(f, x, delta=None):
  """Computes the theoretical and numeric Jacobian of `f`.

  With y = f(x), computes the theoretical and numeric Jacobian dy/dx.

  Args:
    f: the function.
    x: the arguments for the function as a list or tuple of values convertible
      to a Tensor.
    delta: (optional) perturbation used to compute numeric Jacobian.

  Returns:
    A pair of lists, where the first is a list of 2-d numpy arrays representing
    the theoretical Jacobians for each argument, and the second list is the
    numerical ones. Each 2-d array has "y_size" rows
    and "x_size" columns where "x_size" is the number of elements in the
    corresponding argument and "y_size" is the number of elements in f(x).

  Raises:
    ValueError: If result is empty but the gradient is nonzero.
    ValueError: If x is not list, but any other type.

  Example:

  >>> @tf.function
  ... def test_func(x):
  ...   return x*x
  ...
  >>>
  >>> class MyTest(tf.test.TestCase):
  ...
  ...   def test_gradient_of_test_func(self):
  ...     theoretical, numerical = tf.test.compute_gradient(test_func, [1.0])
  ...     # ((array([[2.]], dtype=float32),),
  ...     #  (array([[2.000004]], dtype=float32),))
  ...     self.assertAllClose(theoretical, numerical)

  """
  if not isinstance(x, (list, tuple)):
    raise ValueError(
        "`x` must be a list or tuple of values convertible to a Tensor "
        "(arguments to `f`), not a %s" % type(x))
  if delta is None:
    # By default, we use a step size for the central finite difference
    # approximation that is exactly representable as a binary floating
    # point number, since this reduces the amount of noise due to rounding
    # in the approximation of some functions.
    delta = 1.0 / 1024
  return _compute_gradient_list(f, x, delta)


def max_error(grad1, grad2):
  """Computes maximum elementwise gap.

  Computes the maximum elementwise gap between two lists of tensors of the same
  shape.

  Args:
    grad1: a lists of tensors.
    grad2: a lists of tensors with the same shape as grad1.

  Returns:
    The maximum elementwise gap between the two.
  """
  error = 0
  for j_t, j_n in zip(grad1, grad2):
    if j_t.size or j_n.size:  # Handle zero size tensors correctly
      error = np.maximum(error, np.fabs(j_t - j_n).max())
  return error